We state the consequence of
Corollary REF  in the case of \(S_n\) 
explicitly,
and illustrate this with examples
below.
Fortunately, for the symmetric groups
we have a combinatorial criterion that determines
when two irreducible characters belong to the same \(p\) -block:
this is the case if and only if their labelling partitions
have the same \(p\) -core (see [1]}).
Thus a 2-block \(B\)  of \(S_n\)  is combinatorially
determined by the common 2-core \(\lambda _{(2)}\)  of
all the partitions \(\lambda \)  labelling the irreducible
characters in \({\rm Irr}(B)\) . The common 2-weight
of all these characters \(\lambda \)  is
called the 2-weight \(w=w(B)\)  of \(B\) .
Thus \(n=2w+|\rho |\) .
